Time-varying probabilities of earthquake occurrence in central New Zealand based on the EEPAS model compensated for time-lag

Abstract

SUMMARY The ‘Every Earthquake a Precursor According to Scale’ (EEPAS) model treats every earthquake as a precursor of larger earthquakes to follow it within a time-span ranging from months to decades, depending on magnitude. Each earthquake contributes a transient increment to the expected rate of earthquake occurrence in its vicinity, based on empirical predictive scaling relations associated with the precursory scale increase phenomenon. Incomplete information on precursory earthquakes causes the EEPAS model to underpredict the expected number of earthquakes, in particular when forecasting across a time-lag for periods beginning several years ahead. We demonstrate how the model can be modified to compensate for such time-lags when calculating future forecasts. Given the model parameters, the completeness of precursory information can be expressed as a function of the target earthquake magnitude and the time-lag. We consider two end-members for compensating the model for incompleteness. In one end-member, only the background smoothed-seismicity component of the EEPAS model is compensated, in the other, only the time-varying component of the EEPAS model is compensated. We estimate an optimal mixture of these two end-members for time-lags out to 12 yr, using several different versions of the EEPAS model and subsets of the New Zealand earthquake catalogue to which the models were previously fitted. Performance is checked on an independent test period. The optimal compensated model has increasingly high information gains over the original EEPAS model with increasing time-lags. Using catalogue data complete to 2018, the compensated models forecast increased annual probabilities of earthquake occurrence above magnitude thresholds from 6.0 to 8.0 in central New Zealand in the period 2019–2030 relative to the preceding period 2008–2018.

The Effect of Catalogue Lead Time on Medium-Term Earthquake Forecasting with Application to New Zealand Data

“…Each earthquake ( t i , m i , x i , y i ), with t i greater than a starting time, t 0 , and m i greater than a minimum magnitude, m 0 , contributes a transient increment λ i ( t , m , x , y ) to the future rate density in its vicinity, given by where w i is a weighting factor to emphasise earthquakes that are most likely to be precursors, and f , g and h are densities of the probability distributions derived from the Ψ-predictive scaling relations (Equation (3)) for time, magnitude and location, respectively [ 19 ]. Following the notation of Reference [ 28 ], the magnitude density, g, is a normal density of the form where a M , b M and σ M are parameters, with a M and b M based on the corresponding regression parameters in (3) and σ M on the scatter of points around the regression line in Figure 2 a. The time density, f, is a lognormal density of the form where H ( s ) = 1 if s > 0 and 0 otherwise, and a T , b T and σ T are parameters, with a T and b T based on the corresponding regression parameters in (3) and σ T on the scatter of points around the regression line in Figure 2 b.…”

“…An expression for the completeness of precursory earthquake contributions in the EEPAS model at a given time-lag, T, and a target magnitude, m , was presented in Reference [ 28 ]. The time-lag, T, is the interval between the end of the earthquake catalogue and the target time for which the forecast is being made.…”

“…It was assumed in Reference [ 28 ] that L (at around 7 decades in the examples considered) was long enough so that the contributions to the EEPAS rate density at ( t,m ) from unrecorded precursory earthquakes that might have occurred before the start of the catalogue can be deemed negligible. Here, we make the reverse assumption: that the time-lag, T, is negligibly small and that the lead time, L , from the starting time, t 0 , up to time, t , is short enough so that the contributions from unrecorded precursory earthquakes that might have occurred before t 0 are appreciable.…”